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Arc Length Problem

  1. Mar 15, 2006 #1
    Hey,
    I need some help with an arc length question. It is:
    Find the length of the curve:
    x=3y^(4/3)-(3/32)y^(2/3) from y=125 to y= 216
    So i know i need to use Arc Length=sqrt(1+(dx/dy)^2) but i cant seem to get the right answer.
    I have the derivative as 4y^(1/3)-(1/16)y^(-1/3). Squaring that i get:
    ((4y^(1/3)-(1/16)y^(-1/3))^2
    Then took the square root of one and the square root of the above to get:
    1+4y^(1/3)-(1/16)y^(-1/3). Then I take the integral of this from 125 to 216 and get an answer of 2105.03125, but this isnt right.
    Can someone tell me where i went wrong and point me in the right direction.
    Thanks
     
  2. jcsd
  3. Mar 15, 2006 #2
    the square root of x^2 + y^2 doesn't equal the square root of x^2 plus the square root of y^2. The square root of 25 plus 25 equals the square root of 50 which doesn't equal 10 (the square root of 25 + the square root of 25) just an example.
     
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